The invention relates to dielectric mirrors used in laser systems.
An objective of certain types of laser systems is generation of extremely short laser pulses, such as femtosecond pulses. Femtosecond laser pulses are useful in a wide range of technologies, including signal processing, high speed communications, optical imaging, and optical accelerators. As laser system engineers continue to generate shorter and shorter pulses, the frontiers of the above technologies continue to expand.
Laser systems that generate broadband ultra-short pulses must include reflective structures, e.g., mirrors, that achieve high reflectivity over a broad wavelength range. In general, the broadband reflective mirrors in such laser systems are Bragg mirrors that have been modified to control group delay dispersions (GDDs).
Referring to FIG. 1, a standard dielectric Bragg mirror 10 includes alternating high refractive index and low refractive index layers, such as alternating TiO2/SiO2 layers 12 and 14. Each layer has a thickness of xcexB/4, where xcexB is the Bragg wavelength of the mirror. The high reflectivity bandwidth of standard Bragg mirror 10, however, is only about 200 nm at a center wavelength of 800 nm. The useful high reflectivity bandwidth is further limited (e.g., to about 100 nm) by higher order GDDs produced by standard Bragg mirrors. The bandwidth of an ultra-short pulse generated by a laser system using mirror 10, therefore, will also be unacceptably limited.
To expand the useful high reflectivity bandwidth of standard Bragg mirrors, designers began xe2x80x9cchirpingxe2x80x9d the layer pairs in the mirror. Referring to FIG. 2, in a simple chirped mirror 30, the thickness Tn of individual layer pairs varies along the length of the mirror, shortening toward the front 32 of mirror 30. As a result, longer wavelengths penetrate deeper into the mirror than shorter wavelengths before being reflected, allowing mirror 30 to reflect an enlarged wavelength range. In addition, the reflection includes a negative dispersion, since the longer wavelengths experience more group delay than the shorter wavelengths. This dispersion compensates for the positive dispersion produced by other cavity components in the laser system, such as the laser crystal.
It turns out, however, that simple chirped mirrors do not produce a smooth, controlled group delay. While the local average of the group delay does increase linearly with increasing wavelength, as expected, it also exhibits strong oscillations. The cause of these oscillations is the following. Longer wavelengths (e.g., xcex2 in FIG. 2) have to pass the first section of the Bragg mirror, which acts as a transmission grating for these wavelengths. Slight reflections of xcex2 from the front section of mirror 30, therefore, interfere with stronger reflections of xcex2 from the back layers, as in a Gires-Tournouis Interferometer (GTI). The oscillations in the group delay caused by the GTI effect have an amplitude of several tens of femtoseconds, making these simple-chirped mirrors less useful for ultra short pulse generation. See Kartner et al., WO 99/60675, which is incorporated herein by reference, and Matuschek et al., xe2x80x9cTheory of Double-Chirped Mirrors,xe2x80x9dIEEE J. of Selected Topics in Quantum Electronics, 4:197-208 (1998).
To compensate for the GTI effect experienced by the longer wavelengths, engineers developed double-chirped mirrors. Referring to FIG. 3, a double-chirped mirror 50 has about 60 alternating high and low refractive index layers 52 and 54. (For clarity, FIG. 3 shows only 24 layers.) As in the simple chirped mirror, the thickness of individual layer pairs varies along the length of mirror 50, decreasing towards a front 56 of the mirror. In addition, the thickness of the high index layers 52 varies relative to the low index layers 54, such that the difference in thickness between the layers in each pair increases towards front 56. This gradual variation in the relative thickness of the high index layers 52 causes a gradual increase, or xe2x80x9cchirping,xe2x80x9d in the coupling coefficient in the front portion, or xe2x80x9cdouble-chirpedxe2x80x9d portion 58, of mirror 50. If the coupling coefficient is chirped along with the period of the grating, then the GTI effect caused by the impedance mismatch in portion 58 of the mirror can be effectively eliminated, thereby substantially reducing oscillations in the group delay found in simple chirped mirrors. Double-chirped mirrors are further described in Matuschek et al., xe2x80x9cAnalytical Design of Double-Chirped Mirrors with Custom-Tailored Dispersion Characteristics,xe2x80x9d IEEE J. of Quantum Electronics, 35:129-37 (1999); and Matuschek et al. (1998), supra, both of which are incorporated herein by reference.
While double chirping does substantially reduce oscillations caused by the impedance mismatch within the double-chirped portion 58 of mirror 50, it does not produce an entirely controlled group delay. The reason is that a second impedance mismatch exists in mirror 50, between the air and front 56 of the mirror. The refractive index jump between air and the first layer 60 at front 56 introduces a reflection and, consequently, a second GTI-like oscillation in the group delay. Matuschek et al. (1998), supra.
To reduce the oscillations caused by the air-mirror mismatch, engineers add a multi-layer anti-reflective (AR) coating 62 to front 56 of the mirror. Id. While the AR coating does taper the impedance, it does not entirely alleviate the mismatch. For a typical laser system, the AR coating 62 must have a very low amplitude reflectivity, r, e.g., less than 0.01, or preferably less than 0.001, to effectively reduce the oscillations caused by the air-mirror mismatch. At present, AR coatings with amplitude reflectivities less than 0.01 are expensive, and can only be achieved over a wavelength range of about 350 nm. AR coatings with amplitude reflectivities below 0.001 are not yet possible. Double-chirped mirrors with AR coatings, therefore, do not adequately reduce GTI-like oscillations caused by the air-mirror mismatch over a bandwidth greater than about 350 nm at a center wavelength of 800 nm, which is about half an octave in the frequency domain.
In general, in one aspect, the invention features a mirror system for use in generating a short duration laser pulse. The system includes first and second double-chirped mirrors disposed along an optical path within a cavity, where the second double-chirped mirror includes an additional phase-shifting layer as compared to the first double-chirped mirror. The additional phase-shifting layer causes the mirror system during use to produce a laser pulse that is characterized by oscillations in group delay substantially reduced in amplitude in comparison to oscillations in group delay for a pulse produced by the same system without the additional phase-shifting layer.
Embodiments of this aspect of the invention may include one or more of the following features. The additional phase-shifting layer can have a thickness of about xc2xc of a center wavelength of the mirror. The mirrors can be computer optimized so that reflections from the mirrors have equal average group delay dispersions, but opposite oscillations in group delay dispersion over substantially all wavelengths reflected by the mirrors.
The oscillations in group delay substantially reduced in amplitude by inclusion of the additional phase-shifting layer are caused by, e.g., impedance mismatches between air and the double-chirped mirrors. The additional phase-shifting layer reduces overall oscillations by causing the oscillations in group delay resulting from the impedance mismatch between air and the second double-chirped mirror to be out of phase (e.g., by xcfx80 over all wavelengths reflected by the mirrors) with oscillations in group delay resulting from the impedance mismatch between air and the first double-chirped mirror.
In another aspect, the invention features a mirror system for use in generating a short duration laser pulse. The system includes a first mirror assembly that has one or more double-chirped mirrors, and a second mirror assembly that also has one or more double-chirped mirrors. The second assembly is arranged relative to the first assembly such that radiation reflected from the first assembly travels to the second assembly. The second assembly includes a phase-shifting element that causes the mirror system during use to produce a laser pulse having oscillations in group delay that are substantially reduced in amplitude in comparison to oscillations in group delay for a pulse produced by the same system without the phase-shifting element.
Embodiments of this aspect of the invention may include one or more of the following features. The first and second assemblies can include equal numbers of double-chirped mirrors, e.g., each can include a single mirror. The phase-shifting element can be an additional refractive layer on at least one double-chirped mirror in the second assembly. The additional layer can have a thickness of about xc2xc of the center wavelength of the mirror, and can be formed from a material such as SiO2, TiO2, MgF2, Al2O3, AIF9, HfO2, NbO2, ZrO2, Y2O2, AlO2, or Gd2O3. The radiation reflected from the first assembly can travel directly to the second assembly.
In another aspect, the invention features a laser system that includes a pump, a laser crystal, and first and second double-chirped mirrors disposed on opposite sides of the crystal, such that laser light generated by the crystal reflects between the first and second double-chirped mirrors. The second double-chirped mirror has an additional phase-shifting refractive layer as compared to the first double-chirped mirror.
In another aspect, the invention features a pair of double-chirped mirrors prepared by a process that includes the steps of: (a) providing a computer model of a first double-chirped mirror that reflects over a desired wavelength range; (b) providing a computer model of a second double-chirped mirror that also reflects over the desired wavelength range, where the second double-chirped mirror has an additional layer as compared to the first double-chirped mirror, and the additional layer has a thickness equal to about xc2xc of a center wavelength of the desired wavelength range; (c) optimizing the computer model of the second double-chirped mirror such that oscillations in group delay dispersion produced by the second double chirped mirror are opposite oscillations in group delay dispersion produced by the first double-chirped mirror over substantially all wavelengths in the desired wavelength range; and (d) manufacturing the first and second double-chirped mirrors in accordance with the computer models.
Embodiments of this aspect of the invention may include one or more of the following features. The preparation process can further include optimizing the first double-chirped mirror prior to optimizing the second double-chirped mirror. In addition, the process can further include: (e) adding anti-reflective coatings to the computer models of the first and second double-chirped mirrors after the optimizing step; and (f) re-optimizing the first and second double-chirped mirrors to minimize oscillations in the total group delay dispersion produced by reflection from both the first and second double-chirped mirrors over substantially all wavelengths in the desired wavelength range. The re-optimizing step can include optimizing the anti-reflective coatings of the first and second double-chirped mirrors.
The optimizing step of the preparation process can include optimizing both the first and second double-chirped mirrors simultaneously, and can include varying the thickness of layers in the model of the second double-chirped mirror.
Other embodiments and advantages of the invention will be apparent from the following description and from the claims.